darkSpyro

Post them here!
I may put direct links to recommendations in this post later.

And Yet It Moves - amazing puzzle game
Rayman Origins/Legends - great platforming
Portal 1 and 2 - first person puzzler
Crypt of the NecroDancer - forthcoming rhythm rogue-like dungeon crawler
Okami (PS2 or PS3 HD only) - amazing and beautiful, Zelda-like
Psychonauts - hilarious and fun platforming/combat
Eternal Darkness - great horror

The Saboteur
Mafia II
Red Dead Redemption
Assassin's Creed 3 and 4
The Godfather II
L.A. Noire

NO MORE HEROES

Harvest Moon (the entire series. Each game has it's own gimmick.)
Portal 1 and 2

Brothers: A Tale of Two Sons - Play this game with someone close to you, while sharing the same controller. It's an amazing experience.

Sonic Generations PC - The console version is great and all, but if you have a PC that's powerful enough to run it, get it on that. 60FPS Sonic Generations is amazing, you can install tons of awesome mods with minimal effort using Sonic GMI, and I hear it's even getting Oculus Rift support (lol that will be fun). And considering you can get it as part of the Sonic Franchise bundle on Steam (every Steam Sonic game, plus DLC where applicable, for less than €30. And even cheaper during sales. I got it for €14 in the Autumn sales).

Journey - It's best I don't explain. You really have to experience this for yourself, and make sure you are connected to PSN while you play.

Rayman Legends - Intense, yet accessible platforming action with amazing atmosphere, a soundtrack that will stay with you, graphics that mix cartoony visuals with the artistic finesse of any world renowned painting, tons of unlockables (including the majority of levels from Rayman Origins, which are now looking better in the updated engine), a hilarious football mini-game, and a superb and competitive online challenge mode. Oh, and them music levels. Seriously, this game is just perfect. I recommend it on Wii U if you have friends to play with, or PS Vita if you don't have friends to play with. Both have the added Murfy interaction that the game was designed for, and the other versions lack it.

Sonic All-Stars Racing Transformed - Simply one of the best racing games to come out in a long time. Not just in the kart racer genre, but in general (quite frankly, it has too much demand for actual skill to be considered "just another kart racer"). While Mario Kart is great for fun, this game is great for fun times, and for serious competitive play. And it never feels dull because of the vehicle transformations. Recommended on Wii U or PC (the former has extra modes, a free bonus character and track, Game Pad support, and the largest install base. The latter performs a bit better on a good enough PC, and has the largest character roster, including guests like Team Fortress 2 characters, and Simon from the Yogscast).

LEGO City Undercover - Highly underrated classic for the Wii U. It's basically Grand Theft Auto in a LEGO setting. Tons of platforming and collectibles, tons of vehicles, awesome soundtrack inspired by old buddy cop movies, top notch voice acting, plenty of hilarious references to classic crime movies, plenty of gut busting original jokes, a well put together storyline, and awesome use of the Wii U GamePad.